{
 "cells": [
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Text provided under a Creative Commons Attribution license, CC-BY.  All code is made available under the FSF-approved BSD-3 license.  (c) Lorena A. Barba, Gilbert F. Forsyth 2017. Thanks to NSF for support via CAREER award #1149784."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[@LorenaABarba](https://twitter.com/LorenaABarba)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "12 steps to Navier–Stokes\n",
    "=====\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You see where this is going ... we'll do 2D diffusion now and next we will combine steps 6 and 7 to solve Burgers' equation. So make sure your previous steps work well before continuing."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Step 7: 2D Diffusion\n",
    "----\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here is the 2D-diffusion equation:\n",
    "\n",
    "$$\\frac{\\partial u}{\\partial t} = \\nu \\frac{\\partial ^2 u}{\\partial x^2} + \\nu \\frac{\\partial ^2 u}{\\partial y^2}$$\n",
    "\n",
    "You will recall that we came up with a method for discretizing second order derivatives in Step 3, when investigating 1-D diffusion.  We are going to use the same scheme here, with our forward difference in time and two second-order derivatives. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\frac{u_{i,j}^{n+1} - u_{i,j}^n}{\\Delta t} = \\nu \\frac{u_{i+1,j}^n - 2 u_{i,j}^n + u_{i-1,j}^n}{\\Delta x^2} + \\nu \\frac{u_{i,j+1}^n-2 u_{i,j}^n + u_{i,j-1}^n}{\\Delta y^2}$$\n",
    "\n",
    "Once again, we reorganize the discretized equation and solve for $u_{i,j}^{n+1}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{split}\n",
    "u_{i,j}^{n+1} = u_{i,j}^n &+ \\frac{\\nu \\Delta t}{\\Delta x^2}(u_{i+1,j}^n - 2 u_{i,j}^n + u_{i-1,j}^n) \\\\\n",
    "&+ \\frac{\\nu \\Delta t}{\\Delta y^2}(u_{i,j+1}^n-2 u_{i,j}^n + u_{i,j-1}^n)\n",
    "\\end{split}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy\n",
    "from matplotlib import pyplot, cm\n",
    "from mpl_toolkits.mplot3d import Axes3D ##library for 3d projection plots\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "###variable declarations\n",
    "nx = 31\n",
    "ny = 31\n",
    "nt = 17\n",
    "nu = .05\n",
    "dx = 2 / (nx - 1)\n",
    "dy = 2 / (ny - 1)\n",
    "sigma = .25\n",
    "dt = sigma * dx * dy / nu\n",
    "\n",
    "x = numpy.linspace(0, 2, nx)\n",
    "y = numpy.linspace(0, 2, ny)\n",
    "\n",
    "u = numpy.ones((ny, nx))  # create a 1xn vector of 1's\n",
    "un = numpy.ones((ny, nx))\n",
    "\n",
    "###Assign initial conditions\n",
    "# set hat function I.C. : u(.5<=x<=1 && .5<=y<=1 ) is 2\n",
    "u[int(.5 / dy):int(1 / dy + 1),int(.5 / dx):int(1 / dx + 1)] = 2  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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2m9hmQ86iVLoyNqPvQ6ZV1Y/Szyfbop1QaAOBgO6bGGiNqUUXgGZ3PGI8kq6L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\nhdKZpwAckhLc76GP/BTV/H8ysEDiKGO8QgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6dc29db4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = pyplot.figure()\n",
    "ax = fig.gca(projection='3d')\n",
    "X, Y = numpy.meshgrid(x, y)\n",
    "surf = ax.plot_surface(X, Y, u, rstride=1, cstride=1, cmap=cm.viridis,\n",
    "        linewidth=0, antialiased=False)\n",
    "\n",
    "ax.set_xlim(0, 2)\n",
    "ax.set_ylim(0, 2)\n",
    "ax.set_zlim(1, 2.5)\n",
    "\n",
    "ax.set_xlabel('$x$')\n",
    "ax.set_ylabel('$y$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{split}\n",
    "u_{i,j}^{n+1} = u_{i,j}^n &+ \\frac{\\nu \\Delta t}{\\Delta x^2}(u_{i+1,j}^n - 2 u_{i,j}^n + u_{i-1,j}^n) \\\\\n",
    "&+ \\frac{\\nu \\Delta t}{\\Delta y^2}(u_{i,j+1}^n-2 u_{i,j}^n + u_{i,j-1}^n)\n",
    "\\end{split}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "###Run through nt timesteps\n",
    "def diffuse(nt):\n",
    "    u[int(.5 / dy):int(1 / dy + 1),int(.5 / dx):int(1 / dx + 1)] = 2  \n",
    "    \n",
    "    for n in range(nt + 1): \n",
    "        un = u.copy()\n",
    "        u[1:-1, 1:-1] = (un[1:-1,1:-1] + \n",
    "                        nu * dt / dx**2 * \n",
    "                        (un[1:-1, 2:] - 2 * un[1:-1, 1:-1] + un[1:-1, 0:-2]) +\n",
    "                        nu * dt / dy**2 * \n",
    "                        (un[2:,1: -1] - 2 * un[1:-1, 1:-1] + un[0:-2, 1:-1]))\n",
    "        u[0, :] = 1\n",
    "        u[-1, :] = 1\n",
    "        u[:, 0] = 1\n",
    "        u[:, -1] = 1\n",
    "\n",
    "    \n",
    "    fig = pyplot.figure()\n",
    "    ax = fig.gca(projection='3d')\n",
    "    surf = ax.plot_surface(X, Y, u[:], rstride=1, cstride=1, cmap=cm.viridis,\n",
    "        linewidth=0, antialiased=True)\n",
    "    ax.set_zlim(1, 2.5)\n",
    "    ax.set_xlabel('$x$')\n",
    "    ax.set_ylabel('$y$');\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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a204LShXCIdbNiha2QwjITbrN6gLZCC1LuoIgoKoqHo8nF/RpBNxbb1EUCYfD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BpNlGRttks6/4Q/vEnXEO6IG+lr75c63xnZWSDpcZ3ZDhr3H8eRbSfBEY8owoBnCIPFQG/bwKwd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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6dbffcc208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diffuse(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NhCSWeQKofzuT3UazF6X2GsrprZ254p0en04a744lXQCv15svpWw2nFu2+3w+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/R3DeEtcZOWaaHxSKdcdnB67QjxOIH2AQRBIH9JNmqtmrb6XhKxBK7cDFQkZOWJVq8hf0kOao2a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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6dbe9df630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diffuse(14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VD27YeuVkVgrz/QAgryel9pu2q7d254r3+vy00vluWegC+Hy+Yiul13Iv2e73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\nWrKRApF+fu7YuAuNJLK9enLtbXYj4RE7rXKdTrXJ3npvsPIEbLh9Fo6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Z7z9XvKTkhWaz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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6dbffaf550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diffuse(50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Learn More"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The video lesson that walks you through the details for Steps 5 to 8 is **Video Lesson 6** on You Tube:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/tUg_dE3NXoY\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7f6dbe83ec88>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('tUg_dE3NXoY')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<link href='http://fonts.googleapis.com/css?family=Fenix' rel='stylesheet' type='text/css'>\n",
       "<link href='http://fonts.googleapis.com/css?family=Alegreya+Sans:100,300,400,500,700,800,900,100italic,300italic,400italic,500italic,700italic,800italic,900italic' rel='stylesheet' type='text/css'>\n",
       "<link href='http://fonts.googleapis.com/css?family=Source+Code+Pro:300,400' rel='stylesheet' type='text/css'>\n",
       "<style>\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n",
       "    }\n",
       "    div.cell{\n",
       "        width:800px;\n",
       "        margin-left:16% !important;\n",
       "        margin-right:auto;\n",
       "    }\n",
       "    h1 {\n",
       "        font-family: 'Alegreya Sans', sans-serif;\n",
       "    }\n",
       "    h2 {\n",
       "        font-family: 'Fenix', serif;\n",
       "    }\n",
       "    h3{\n",
       "\t\tfont-family: 'Fenix', serif;\n",
       "        margin-top:12px;\n",
       "        margin-bottom: 3px;\n",
       "       }\n",
       "\th4{\n",
       "\t\tfont-family: 'Fenix', serif;\n",
       "       }\n",
       "    h5 {\n",
       "        font-family: 'Alegreya Sans', sans-serif;\n",
       "    }\t   \n",
       "    div.text_cell_render{\n",
       "        font-family: 'Alegreya Sans',Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
       "        line-height: 135%;\n",
       "        font-size: 120%;\n",
       "        width:600px;\n",
       "        margin-left:auto;\n",
       "        margin-right:auto;\n",
       "    }\n",
       "    .CodeMirror{\n",
       "            font-family: \"Source Code Pro\";\n",
       "\t\t\tfont-size: 90%;\n",
       "    }\n",
       "/*    .prompt{\n",
       "        display: None;\n",
       "    }*/\n",
       "    .text_cell_render h1 {\n",
       "        font-weight: 200;\n",
       "        font-size: 50pt;\n",
       "\t\tline-height: 100%;\n",
       "        color:#CD2305;\n",
       "        margin-bottom: 0.5em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "    }\t\n",
       "    .text_cell_render h5 {\n",
       "        font-weight: 300;\n",
       "        font-size: 16pt;\n",
       "        color: #CD2305;\n",
       "        font-style: italic;\n",
       "        margin-bottom: .5em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "    }\n",
       "    \n",
       "    .warning{\n",
       "        color: rgb( 240, 20, 20 )\n",
       "        }  \n",
       "</style>\n",
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\"]\n",
       "                           },\n",
       "                tex2jax: {\n",
       "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.core.display import HTML\n",
    "def css_styling():\n",
    "    styles = open(\"../styles/custom.css\", \"r\").read()\n",
    "    return HTML(styles)\n",
    "css_styling()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> (The cell above executes the style for this notebook.)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
